Worked solution · Exam FM
This Exam FM sample reference tests Bond with Geometrically Growing Coupons. At a half-year yield of 3.1%, the redemption has present value 400.17. The remaining price supports thirty coupons growing 1% each period, which makes the first coupon 113.75 and selects choice B.
Independent solution
Setup
Let q be the yield per half-year and index the thirty coupon dates by k.
Model
Separate the growing coupon stream from the redemption payment.
Compute
The coupon coefficient is 21.9350891 and the redemption present value is 400.1659.
Answer
The first coupon rounds to 114, which is choice B.
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30 original bonds problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A ten-year note pays semiannual coupons. The first coupon is 60, each later coupon is 0.5% larger, and the note redeems for 1,000. Investors require a nominal annual yield of 5% convertible semiannually. Determine the note's price.
Discounting twenty coupons growing 0.5% per half-year and the 1000 redemption at 2.5% per half-year gives 1587.41, choice C.
Setup
There are twenty half-year periods and the periodic yield is 2.5%.
Model
Write the price as a growing coupon sum plus redemption.
Compute
Evaluate both components at the same valuation date.
Answer
The note price is 1587.41, choice C.
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